Godel's Incompleteness Theorems

Raymond M. Smullyan

Godel's Incompleteness Theorems

Raymond M. Smullyan

Description

Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.

Godel's Incompleteness Theorems

Raymond M. Smullyan

Table of Contents

1. The General Idea Behind Gdel's Proof2. Tarski's Theorem for Arithmetic3. The Incompleteness of Peano Arithmetic with Exponentation4. Arithmetic Without the Exponential5. Gdel's Proof Based on Consistency6. Rosser Systems7. Shepherdson's Representation Theorems8. Definability and Diagonalization9. The Unprovability of Consistency10. Some General Remarks on Provability and Truth11. Self-Referential Systems